Coupled FEM-BEM Approach for Axisymetrical Heat Transfer Problems

2008 ◽  
Vol 273-276 ◽  
pp. 740-745
Author(s):  
Gennady Mishuris ◽  
Michał Wróbel
Keyword(s):  
Heat Transfer ◽  
Half Space ◽  
Integral Transform ◽  
Transfer Problem ◽  
Mixed Boundary ◽  
Nonlocal Boundary ◽  
Fem Analysis ◽  
Nonlocal Boundary Conditions ◽  
Problem Solution ◽  
Infinite Domain

This work deals with a stationary axisymmetrical heat transfer problem in a combined domain. This domain consists of half-space joined with a bounded cylinder. An important feature of the problem is the possible flux singularity along the edge points of the transmission surface. Domain decomposition is used to separate the subdomains. The solution for an auxiliary mixed boundary value problem in the half space is found analytically by means of Hankel integral transform. This allows us to reduce the main problem in the infinite domain to another problem defined in the bounded subdomain. In turn, the new problem contains a nonlocal boundary conditions along the transmission surface. These conditions incorporate all basic information about the infinite sub-domain (material properties, internal sources etc.). The problem is solved then by means of the Finite Element Method. In fact it might be considered as a coupled FEM-BEM approach. We use standard MATLAB PDE toolbox for the FEM analysis. As it is not possible for this package to introduce directly a non-classical boundary condition, we construct an appropriate iterative procedure and show the fast convergence of the main problem solution. The possible solution singularity is taken into account and the corresponding intensity coefficient of the heat flux is computed with a high accuracy. Numerical examples dealing with heat transfer between closed reservoir (filled with some substance) and the infinite foundation are discussed.

scholarly journals The inverse coefficient problem of heat transfer in layered nanostructures

2017 ◽  
Vol 20 (3) ◽  
pp. 213-219
Author(s):  
K. K. Abgarian ◽  
R. G. Noskov ◽  
D. L. Reviznikov
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Thermal Resistance ◽  
Transfer Problem ◽  
Dominant Role ◽  
Rapid Development ◽  
Problem Solution ◽  
Microwave Range ◽  
Contact Thermal Resistance ◽  
Resistance Coefficients

The rapid development of electronics leads to the creation and use of electronic components of small dimensions, including nanoelements of complex, layered structure. The search for effective methods for cooling electronic systems dictates the need for the development of methods for the numerical analysis of heat transfer in nanostructures. A characteristic feature of energy transfer in such systems is the dominant role of contact thermal resistance at interlayer interfaces. Since the contact resistance depends on a number of factors associated with the technology of heterostructures manufacturing, it is of great importance to determine the corresponding coefficients from the results of temperature measurements.The purpose of this paper is to evaluate the possibility of reconstructing the thermal resistance coefficients at the interfaces between layers by solving the inverse problem of heat transfer.The complex of algorithms includes two major blocks — a block for solving the direct heat transfer problem in a layered nanostructure and an optimization block for solving the inverse problem. The direct problem was formulated in an algebraic (finite difference) form under the assumption of a constant temperature within each layer, which is due to the small thickness of the layers. The inverse problem was solved in the extreme formulation, the optimization was carried out using zero-order methods that do not require the calculation of the derivatives of the optimized function. As a basic optimization algorithm, the Nelder—Mead method was used in combination with random restarts to search for a global minimum.The results of the identification of the contact thermal resistance coefficients obtained in the framework of a quasi-real experiment are presented. The accuracy of the identification problem solution is estimated as a function of the number of layers in the heterostructure and the «measurements» error.The obtained results are planned to be used in the new technique of multiscale modeling of thermal regimes of the electronic component base of the microwave range, when identifying the coefficients of thermal conductivity of heterostructure.

Analytical Modeling of Heat Transfer in Polycrystalline Diamond Compact Cutters in Rock Turning Processes

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Demeng Che ◽  
Kornel Ehmann ◽  
Jian Cao
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Transfer Problem ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Polycrystalline Diamond ◽  
Experimental Tests ◽  
Rock Cutting ◽  
Polycrystalline Diamond Compact ◽  
Temperature Responses

Heat transfer phenomena at the rock–cutter interface are extremely significant since they affect the polycrystalline diamond compact (PDC) cutter's performance in rock cutting/drilling processes. The understanding of how temperature and heat flux responses in the cutter influence the intrinsic mechanisms of the rock–cutter interactions is an essential prerequisite for providing insights to enhance the performance of PDC cutters and to optimize rock cutting/drilling processes. In this paper, a mixed boundary value heat transfer problem was formulated to analytically describe the heat transfer phenomena in the PDC cutters during two-dimensional (2D) orthogonal rock cutting under steady state conditions. An analytical solution in the form of an infinite series was derived based on the method of separation of variables, the use of appropriate simplifications in the formulated problem and the separation of the thermal from the mechanical phenomena. A series of experimental tests were conducted on a newly developed rock cutting testbed to calibrate the process parameters in the analytical solution and then to confirm the validity of the assumed boundary conditions. The comparison between the newly derived analytical solution and the experimental data shows a good match in terms of temperature responses during rock cutting performed by PDC cutters.

scholarly journals Benchmark Studies for the Generalized Streamwise Periodic Heat Transfer Problem

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Steven B. Beale
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Transfer Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Wall Boundary Conditions ◽  
Engineering Problems ◽  
Complex Engineering ◽  
The Common ◽  
Periodic Heat

This is a comparison of calculations performed with a scheme for handling streamwise-periodic boundary conditions with known solutions to the common problem of fully developed heat transfer in a plane duct. Constant value, constant flux, mixed boundary conditions, and linear wall flux (conjugate heat transfer) are all considered. Agreement is, in every case, near exact showing that the methodology may be applied with confidence to complex engineering problems with a variety of thermal wall boundary conditions.

scholarly journals An integral transform applied to solve the steady heat transfer problem in the half-plane

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 105-111
Author(s):  
Tongqiang Xia ◽  
Shengping Yan ◽  
Xin Liang ◽  
Pengjun Zhang ◽  
Chun Liu
Keyword(s):  
Heat Transfer ◽  
Half Plane ◽  
Laplace Equation ◽  
Integral Transform ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Linear Heat ◽  
Transfer Problems ◽  
Steady Heat

An integral transform operator U[?(t)= 1/? ???? ?(t)?-i?t dt is considered to solve the steady heat transfer problem in this paper. The analytic technique is illustrated to be applicable in the solution of a 1-D Laplace equation in the half-plane. The results are interesting as well as potentially useful in the linear heat transfer problems.

scholarly journals A new integral transform with an application in heat-transfer problem

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 677-681 ◽  
Author(s):  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Integral Transform ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
First Time

In this paper, an new integral transform J[?(?)] =1/? ?0??(?)e??? d? is proposed for the first time. The integral transform is used to solve the differential equation arising in heat-transfer problem.

Interaction between a Rigid Cylinder with a Piezoelectric Half-Space with Partial Adhesion

2008 ◽  
Vol 33-37 ◽  
pp. 333-338 ◽  
Author(s):  
Zuo Rong Chen ◽  
Shou Wen Yu
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Contact Region ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Dual Integral Equations ◽  
Slip Region

An axisymmetric problem of interaction of a rigid rotating flat ended punch with a transversely isotropic linear piezoelectric half-space is considered. The contact zone consists of an inner circular adhesion region surrounded by an outer annular slip region with Coulomb friction. Beyond the contact region, the surface of the piezoelectric half-space is free from load. With the aid of the Hankel integral transform, this mixed boundary value problem is formulated as a system of dual integral equations. By solving the dual integral equations, analytical expressions for the tangential stress and displacement, and normal electric displacement on the surface of the piezoelectric half-space are obtained. An explicit relationship between the radius of the adhesion region, the angle of the rotation of the punch, material parameters, and the applied loads is presented. The obtained results are useful for characterization of piezoelectric materials by micro-indentation and micro-friction techniques.

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